plane disappears during animation
Action (animation) actuators need to be part of the object, which you want to animate.

In the .blend, the animations are applied to the "ground" plane instead.

To make objects interact with each other in the logic editor, select them at the same time using Shift + Leftclick in the Outliner:



You will see the objects in the logic editor:



Then edit the logic so that one object's controller controls other objects' actuators:



You can see the full process in this video. 
Unfortunately two of the arrows don't animate correctly and I'm not sure why that is. Perhaps their transformations need to be applied?